Question

solve the system given:
3x - y = 7
2x + y = 3

Explanation:

Step1: Add the two equations

We have the system of equations:
$$3x - y = 7$$
$$2x + y = 3$$
Adding them together to eliminate \(y\):
$$(3x - y)+(2x + y)=7 + 3$$
Simplifying the left - hand side: \(3x- y+2x + y=5x\), and the right - hand side is \(10\). So we get \(5x=10\).

Step2: Solve for \(x\)

From \(5x = 10\), divide both sides by \(5\):
\(x=\frac{10}{5}=2\)

Step3: Substitute \(x = 2\) into one of the equations to solve for \(y\)

Let's substitute \(x = 2\) into the equation \(2x + y=3\).
Substitute \(x = 2\) into \(2x + y\): \(2\times2+y=3\), which simplifies to \(4 + y=3\).
Subtract \(4\) from both sides: \(y=3 - 4=-1\)

Answer:

\((2,-1)\)